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The 12th Summer Conference on General Topology and its Applications
August 12-16, 1997
Nipissing University
North Bay, ON, Canada

Organizers
Ted Chase, Boguslaw Schreyer, Jodi Sutherland, Murat Tuncali, Stephen Watson

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Countable Toronto Spaces
by
Gary Gruenhage
Auburn University

We show that for each \alpha < \omega1, it is consistent that there is an \alpha-Toronto space T\alpha, i.e., T\alpha is scattered of Cantor-Bendixon rank \alpha and is homeomorphic to each of its subspaces of the same rank. This gives a consistent answer to a question of J. Steprans. The existence of the spaces T\alpha turns out to follow from the existence of a filter on \omega having some special properties.

Date received: June 23, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caao-21.